When the number of players is small in a weighted majority voting game, it can occur that one of the players has no influence on the result of the vote, in spite of a strictly positive weight. Such a player is called a “dummy” player in game theory. The purpose of this paper is to...

In this paper we compare five well-known methods of apportionment, advanced respectively by Adams, Dean, Hill, Webster and Jefferson. The criterion used for this comparison is the minimization of the distance between a power vector and a population vector. Power is measured with the well-known...

This paper deals with the non-emptiness of the stability set for any proper voting game. We present an upper bound on the number of alternatives which guarantees the non emptiness of this solution concept. We show that this bound is greater than or equal to the one given by Le Breton and Salles...

We consider voting games as procedures to aggregate individual preferences. We survey positive results on the nonemptiness of the core of voting games and explore other solutions concepts that are basic supersets of the core such as Rubinstein's stability set and two types of uncovered sets. We...